On the Theory of Continuous-Spin Particles: Wavefunctions and Soft-Factor Scattering Amplitudes

TL;DR

This paper develops the theoretical framework for continuous-spin particles (CSPs), providing new equations, wavefunctions, and amplitudes, and explores their potential to mediate long-range forces, extending our understanding beyond helicity particles.

Contribution

It introduces the first consistent equations and wavefunctions for CSPs, enabling further study of their interactions and potential physical implications.

Findings

Derived new CSP equations of motion and wavefunctions

Constructed covariant radiation amplitudes for CSPs

Identified a limit where CSP amplitudes resemble helicity particles

Abstract

The most general massless particles allowed by Poincare-invariance are "continuous-spin" particles (CSPs) characterized by a scale \rho, which at \rho=0 reduce to familiar helicity particles. Though known long-range forces are adequately modeled using helicity particles, it is not known whether CSPs can also mediate long-range forces or what consequences such forces might have. We present sharp evidence for consistent interactions of CSPs with matter: new CSP equations of motion, wavefunctions, and covariant radiation amplitudes. In a companion paper, we use these results to resolve old puzzles concerning CSP thermodynamics and exhibit a striking correspondence limit where CSP amplitudes approach helicity-0, 1 or 2 amplitudes.